Author:
Zsolt Szűcs Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

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Abstract

Our purpose is to show that the various concepts of singularity of representable positive functionals on -algebras coincide, moreover to present a new characterization of singularity by means of Choquet theory of the state space. In the context of singularity, the paper includes an equivalent condition for a representable positive functional to be pure.

  • [1] Bratelli, O. Robinson, D. W. 2002 Operator Algebras and Quantum Statistical Mechanics, Vol I. C- and W-Algebras, Symmetry Groups, Decomposition of States 2 Texts and Monographs in Physics Springer-Verlag New York–Heidelberg.

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  • [2] Dixmier, J. 1977 C -algebras North-Holland Mathematical Library 15 North-Holland publishing Co. Amsterdam–New York–Oxford Translated from the French by F. Jellett.

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  • [3] Gudder, S. P. 1979 A Radon–Nikodym theorem for -algebras Pacific J. Math. 80 141149.

  • [4] Handel van, R. 2009 The stability of quantum Markov filters Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 153172 .

  • [5] Hassi, S. Sebestyén, Z. Snoo de, H. 2009 Lebesgue type decompositions for nonnegative forms J. Functional Analysis 257 38583894 .

  • [6] Henle, M. 1972 A Lebesgue decomposition theorem for C-algebras Canad. Math. Bull. 15 8791 .

  • [7] Hewitt, E. Ross, K. A. 1970 Abstract Harmonic Analysis. Vol. II.: Structure and Analysis for Compact Groups. Analysis on Locally Abelian Compact Groups Die Grundlehren de Mathematischen Wissenschaften 152 Springer-Verlag New York–Berlin.

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  • [8] Kosaki, H. 1985 Lebesgue decomposition of states on a von Neumann algebra American J. Math. 107 697735 .

  • [9] Palmer, T. W. 2001 Banach Algebras and the General Theory of -Algebras II Cambridge University Press.

  • [10] Pedersen, G. K. 1979 C -Algebras and their Automorhpism Groups London Mathematical Society Monographs 14 Academic Press, Inc. London–New York Hartcourt Brace Jovanovich, Publishers.

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  • [11] Sebestyén, Z. 1984 On representability of linear functionals on -algebras Period. Math. Hungar. 15 233239 .

  • [12] Szűcs, Zs., On the Lebesgue decomposition of positive linear functionals, Proc. Amer. Math. Soc., to appear.

  • [13] Szűcs, Zs., The Lebesgue decomposition of representable forms over algebras, J. Operator Theory, to appear.

  • [14] Takesaki, M. 2002 Theory of Operator Algebras I Encyclopaedia of Mathematical Sciences 124 Springer-Verlag Berlin.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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